Mechanical arm system distributed iterative learning control method based on loose alignment condition

Abstract

The invention discloses a mechanical arm system fault-tolerant distributed learning control method based on loose alignment conditions. According to the method, an auxiliary system with loose alignment conditions and compensation input saturation is designed, and a backstepping error, a virtual controller and a compensation error are constructed. An iterative learning controller is designed to control a mechanical arm system and compensate an unknown inertia matrix, parameter uncertainty and disturbance, and convergence of an error system is analyzed by constructing a composite energy function. Compared with a traditional control method needing an accurate mathematical model, the control algorithm provided by the invention is more novel and simple in application condition. When the method is used for repeated task operation, the control precision is effectively improved, and the method has good engineering application value.

Description

Technical Field

[0001] The present invention relates to a control method for a robot arm system, and in particular to a distributed iterative learning control method for a robot arm system based on a loose alignment condition. Background Art

[0002] A robotic arm is a mechanical device that can simulate the movements of a human arm. It is usually composed of a series of joints and actuators, and can perform precise and flexible operations in industrial production, medical surgery, logistics and other fields. The design of the robotic arm can be customized according to different needs and application scenarios. Some robotic arms are also equipped with sensors and vision systems to sense and perform tasks more accurately. In modern industry, robotic arms have become important automation equipment that can improve production efficiency, reduce costs, and complete some tasks that are dangerous or arduous for humans.

[0003] Robotic arm control needs to ensure that the robot can accurately reach the specified position or posture when performing tasks and maintain stability, especially in high-speed motion or complex environments. For certain tasks that require real-time response, such as operations on industrial production lines, the robot control system needs to be able to execute instructions quickly and accurately to avoid production interruptions or damage to equipment. When working with humans or other equipment, the robot arm needs to be safe and avoid accidental injury or damage. The robot arm needs to be able to adapt to different working environments and task requirements, including workpieces of different shapes and sizes, as well as possible external interference and obstacles. Solving these difficulties requires comprehensive consideration of multiple factors such as mechanical structure design, control algorithm optimization, and sensor technology application, and requires continuous research and improvement. Summary of the invention

[0004] The purpose of the present invention is to propose a distributed iterative learning control method for a robotic arm system based on loose alignment conditions, which can effectively solve the problems of dynamics, motion planning, disturbance influence, etc. of the robotic arm system and achieve good control effect.

[0005] The specific technical solution of the present invention is as follows: A distributed iterative learning control method for a robotic arm system based on a loose alignment condition comprises the following steps:

[0006] The robotic arm system model is shown below:

[0007] In the formula, x 1，j,k x 2,j,k Denote the joint position and joint velocity of the j-th robot arm, respectively, and D j，k represents the inertia matrix, C j，k represents the centripetal Coriolis matrix, G j，k represents the gravity vector, Fj，k represents disturbance, represents the controller with input saturation, k represents the number of system iterations;

[0008] The traditional alignment condition requires the reference orbit to be spatially closed, so it cannot be applied to iteratively changing reference orbits. Based on this, a loose alignment condition that can handle such reference orbits is designed: x 1,d,k =x 1,r，k -ω1(x 1，r，k (0)-x 1，r，k-1 (T))-ω2(x 2，r，k (0)-x 2，r,k-1 (T))

[0009] In the formula, x 1，d,k 、x 1,r,k They represent the modified reference orbit and the reference orbit respectively, ω1 and ω2 represent the modification functions, which meet the following requirements: ω1(0)=1,ω1(T a )=0,ω1(t)=0,t∈[T a , T] · ω2(0)=0,ω2(T a )=0,ω2(t)=0,t∈[T a , T] ·

[0010] Where T a Indicates the modified length and satisfies 0 <T a ≤T, T is the length of time for each iteration;

[0011] The auxiliary system designed to compensate for input saturation is shown below:

[0012] In the formula, δ 1，j,k ,δ 2,j，k represents the state given by the known auxiliary system, Γ 1，j , Γ 2，J represents the feedback gain to be designed, ε j =1 / 0 indicates whether the j-th robot can obtain information from the reference track, d j represents the relative degree of the j-th robot arm, Δu j，k Represents the difference between the saturated input and the actual input;

[0013] The backstepping error is constructed as follows:

[0014] In the formula, a jl =1 / 0 indicates whether the j-th robot can obtain information from the l-th robot, α 1,j,k Represents a virtual controller and has the following form:

[0015] The construction compensation error is as follows: s i，j，k =z i，j，k -δ i,j，k , i=1,2

[0016] An iterative learning controller is established to control the robotic arm system and compensate for the unknown inertia matrix, parameter uncertainties, and disturbances as shown below:

[0017] In the formula, proj represents the upper and lower bounds of parameter updates, γ 1，j , γ 2,j represents the learning gain that needs to be designed, Xi represents the convergence sequence of series, where q>0, l>2. The convergence of the error system is analyzed by constructing a composite energy function. The specific steps are as follows;

[0018] C001: Define the Lyapunov function of subsystem 1:

[0019] C002: V 1，k Take the derivative:

[0020] C003: Define the Lyapunov function of subsystem 2:

[0021] C004: V 2，k Take the derivative:

[0022] C006: Select a composite energy function of the following form: E j，k (t) = E 1，j，k +E 2，j，k +E 3，j，k E 1,j,k (t) = V 1,j,k +V 2，j，k

[0023] C007: In the formula,

[0024] C008: Consider the E between the kth and k-1th times j，k (t) difference ΔE j，k (t), where:

[0025] C009: According to C008, the following formula can be obtained:

[0026] C010: Further, give E j，1 And the boundedness proof of W1:

[0027] C011: According to C009 and C010, the following formula can be obtained:

[0028] C012: According to C011, the convergence form of the compensation error can be obtained as follows: BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Figure 1 is a flow chart of a method according to an embodiment of the present invention;

[0030] Figure 2 A schematic diagram of a robotic arm system according to an embodiment of the present invention;

[0031] Figure 3 This is a position error convergence diagram of 35 iterations of the method proposed in the present invention in the embodiment;

[0032] Figure 4 This is a velocity error convergence diagram of 35 iterations of the method proposed in the present invention in the embodiment; DETAILED DESCRIPTION

[0033] The present invention is further explained below in conjunction with specific embodiments. It should be understood that these embodiments are only used to illustrate the present invention and are not used to limit the scope of the present invention. After reading the present invention, various equivalent forms of modifications to the present invention by those skilled in the art all fall within the scope defined by the claims attached to this application.

[0034] like Figure 1 As shown, a distributed iterative learning control method for a robotic arm system based on a loose alignment condition includes the following steps:

[0035] Step 1: Set the initial value of the parameter;

[0036] Step 2: Update algorithm parameters;

[0037] Step 3: Generate control input u in real time based on updated algorithm parameters j，k (t);

[0038] Step 4: According to the control input u j，k (t) The tracking error and compensation error generated are used to update the algorithm parameters synchronously;

[0039] Step 5: Repeat steps 3 and 4 until the current iteration ends and the next iteration begins;

[0040] Step 6: An embodiment of the present invention is described below: Considering the fault-tolerant iterative learning control problem of the robotic arm system based on the balance factor, the corresponding mathematical model is:

[0041]

[0042] The system parameters are: x 1,j,k x 2，j，k Denote the joint position and joint velocity of the j-th robot arm, respectively, and D j，k represents the inertia matrix, C j，k represents the centripetal Coriolis matrix, G j，k represents the gravity vector, F j，k represents disturbance, represents the controller with input saturation, k represents the number of system iterations;

[0043] The desired reference orbit is: x 1，r,k (t) = [2sin(t) + 0.05cos(k); 3coS(t) + 0.01cos(k)]; the expected running time T of the system is 2πs;

[0044] Figure 1 is a flow chart of a method according to an embodiment of the present invention; Figure 2 Schematic diagram of a robotic arm system according to an embodiment of the present invention; applying the proposed method, Figure 3 , 4 The position and velocity error convergence diagrams of the proposed method after 35 iterations are shown respectively. From these two figures, it can be seen that the proposed method has a good application effect in the manipulator system, and after the 10th iteration, a satisfactory tracking performance can be obtained.

[0045] References

[0046] [1]D.Shen,J-X.Xu.Distributed learning consensus for heterogenoushigh-order nonlinear multi-agent systems with output constraints.Automatica,vol.97,pp.64-72,2018.

[0047] [2]X.Jin.Formation-based decentralized iterative learning cooperativeimpedance control for a team of robot manipulators.IEEE Transactions onSystems,Man,and Cybernetics:Systems,vol.53,pp.872-881,2023.

Claims

1. A distributed iterative learning control method for a robotic arm system based on loose alignment conditions, characterized in that: The following steps are involved: Design an auxiliary system with relaxed alignment conditions and compensation for input saturation, construct backstepping error, virtual controller and compensation error; Design an iterative learning controller to control the manipulator system and compensate for the unknown inertia matrix, parameter uncertainties, and disturbances; A composite energy function is constructed to analyze the convergence of the error system.

2. The distributed iterative learning control method for a robotic arm system based on loose alignment conditions according to claim 1 is characterized in that: Design an auxiliary system with loose alignment conditions and compensation for input saturation, construct backstepping error, compensation error and virtual controller. The specific steps are as follows: Consider the following system with j robotic arms: In the formula, x 1，j，k x 2，j，k Denote the joint position and joint velocity of the j-th robot arm, respectively, and D j，k represents the inertia matrix, C j，k represents the centripetal Coriolis matrix, G j，k represents the gravity vector, F j，k represents disturbance, represents the controller with input saturation, and k represents the number of system iterations. The traditional alignment condition requires the reference orbit to be spatially closed, so it cannot be applied to iteratively changing reference orbits. Based on this, a loose alignment condition that can handle such reference orbits is designed: x 1，d，k =x 1，r，k -ω1(x 1,r,k (0)-x 1，r，k-1 (T))-ω2(x 2，r，k (0)-x 2，r，k-1 (T)) In the formula, x 1，d，k 、x 1,r,k denote the modified reference orbit and the reference orbit respectively, ω1 and ω2 denote the modification functions, which meet the following requirements: ·ω1(0)=1,ω1(T a )=0,ω1(t)=0,t∈[T a ,T] · ·ω2(0)=0,ω2(T a )=0,ω2(t)=0,t∈[T a ,T] · Where T a Indicates the modified length and satisfies 0 <T a ≤T, where T is the length of time for each iteration. The auxiliary system designed to compensate for input saturation is shown below: In the formula, δ 1，j，k , δ 2，j，k represents the state given by the known auxiliary system, Γ 1，j , Γ 2，j represents the feedback gain to be designed, ε j =1 / 0 indicates whether the j-th robot can obtain information from the reference track, d j represents the relative degree of the j-th robot arm, Δu j，k Represents the difference between the saturated input and the actual input. The backstepping error is constructed as follows: In the formula, a jl =1 / 0 indicates whether the j-th robot can obtain information from the l-th robot, α 1，j，k Represents a virtual controller and has the following form: The construction compensation error is in the following form: s i，j，k =z i,j，k -δ i，j,k ,i=1,2 3. The distributed iterative learning control method for a robotic arm system based on loose alignment conditions according to claim 2 is characterized in that: An iterative learning controller is designed to control the robotic arm system and compensate for the unknown inertia matrix, parameter uncertainty and disturbance. The convergence of the error system is analyzed by constructing a composite energy function. The specific steps are as follows: An iterative learning controller is established to control the robotic arm system and compensate for the unknown inertia matrix, parameter uncertainties, and disturbances as shown below: In the formula, proj represents the upper and lower saturation limits of the parameters, γ 1,j , γ 2，j represents the learning gain that needs to be designed, represents a sequence of convergent series, where q>0 and l>2.

4. The distributed iterative learning control method for a robotic arm system based on loose alignment conditions according to claim 3 is characterized in that: The convergence of the error is analyzed by constructing a composite energy function. The specific steps are as follows: B001: Define the Lyapunov function of subsystem 1: B002: V 1，k Take the derivative: B003: Define the Lyapunov function of subsystem 2: B004: V 2，k Take the derivative: B005: Select a composite energy function of the following form: AND j，k (t)=And 1，j，k +E 2，j，k +E 3,j,k E 1,j,k (t)=V 1,j,k +V 2,j,k B006: In the formula, B007: Consider the E between the kth and k-1th times j，k (t) difference ΔE j，k (t), where: B008: According to B007, the following formula can be obtained: B009: Further, give E j,1 And the boundedness proof of W1: B010: According to B008 and B009, the following formula can be obtained: B011: According to B010, the convergence form of the compensation error can be obtained as follows:

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